RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Raw Material Amount Available for Production Material 1 20 tons Material 2 5 tons Material 3 21 tons Assuming that RMC is interested in maximizing the total profit contribution, answer the following: i. Compute the value of the objective function when 1 ton is added to the original amount available for production of raw material 1. Also, find the corresponding dual price dual price. j. Compute the range where the dual price computed in (i) remains valid. k. Compute the range of optimality for the objective function coefficients.
RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products:
a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material
1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of
material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is
$40 for every ton of fuel additive produced and $30 for every ton of solvent base produced.
RMC’s production is constrained by a limited availability of the three raw materials. For
the current production period, RMC has available the following quantities of each raw material:
Raw Material Amount Available for Production
Material 1 20 tons
Material 2 5 tons
Material 3 21 tons
Assuming that RMC is interested in maximizing the total profit contribution, answer the
following:
i. Compute the value of the objective function when 1 ton is added to the original
amount available for production of raw material 1. Also, find the corresponding dual
price dual price.
j. Compute the range where the dual price computed in (i) remains valid.
k. Compute the range of optimality for the objective function coefficients.
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